Electrical circuits and other samples may include multiple microscopic structures such as bumps that should be measured for various purposes.
FIG. 1 illustrates a prior art portion 10 of a semiconductor chip with multiple solder bumps.
A bump has a shape that may be approximated by a dome. The manufacturing process of the bump mandates certain height to diameter ratios of the bump.
There are several known optical height metrology methods. The most sensitive methods are based on phase detection using various interferometric principles.
It is known in the art that the measurement of phase is a noisy process and that phase information is noisy. This noise can be more severe when measuring structures such as bumps due to their shape.
Digital holographic microscopes such as the DHM R1100™ of Lyncee Tec of Lausanne Switzerland use two laser sources that can be simultaneously or alternatively switched or continuously operate to illuminate a sample. Light from the sample and references beams are processed to provide phase information and amplitude information. The structure of the DHM R1100 is described in “Digital holographic reflectometry”. Optics Express Vol. 18, No. 4, 15 Feb. 2010, which is incorporated herein by reference.
The mentioned above interferometric based optical height metrology method can measure a height maximum range that is limited by the wavelength of the light. The optical phenomena that limit the range called “phase warp”.
There are numerous methods known for “phase un-warp” algorithm, all use various assumptions about phase continuity. Such methods are not applicable to bump metrology due to intrinsic phase discontinuity due to bump geometry.
The phase information exhibits phase ambiguity. FIGS. 2a and 2b illustrate phase height ambiguities for two different phase offsets.
Curve 22 of FIG. 2a and curve 24 of FIG. 2b represent the relationship between phase information (y-axis) and height (x-axis) of a microscopic structure represented by the phase information.
Phase information can be defined in a range of 2 pi (the phase can range between minus pi and plus pi), while “phase offset” (PO) defines the starting point of the phase extraction algorithm.
FIG. 2a illustrates the relationship between phase information and height obtained by an calculation based on and image created by interferometer that is set to have a phase offset of zero while FIG. 2b illustrates this relationship for a phase offset of minus pi.
The relationship can be defined similarly for any phase offset in a given range. Eventually, the linear slope of this relationship is specifically defined for any optical setup.
FIGS. 2a and 2b illustrate that there is intrinsic height uncertainty exists in this kind of behavior. A phase range that spans between minus pi and plus pi is mapped to height ranges each having a range size of Hr. In this case the same phase information value shall be measured for different heights located at the same position (offset from the beginning of the height range) at different height ranges.
In mathematical terms and assuming the Hm is the measured height then:Phase(Hm)=phase(Hm+N*Hr).
More than that, FIGS. 2a and 2b show discontinuities—“phase warp”—a jump from—pi to +pi. When operating at there discontinuities the height measurement will suffer from possible errors as small noises can result in a very large offset in the height measurement. For example, for PO=0, the discontinuity is located around any modulo of ½ Hr—at any height that can be represented by Hr*(0.5+N), N being a positive integer.
There is a growing need to provide fast and accurate means for measuring the height of microscopic structures.